We present new full-sky temperature maps in five frequency bands from 23 to 94GHz, based on data from the first 3 years of the WMAP sky survey. The new maps are consistent with the first-year maps and are more sensitive. We employ two forms of multifrequency analysis to separate astrophysical foreground signals from the CMB, each of which improves on our first-year analyses. First, we form an improved "Internal Linear Combination" (ILC) map, based solely on WMAP data, by adding a bias-correction step and by quantifying residual uncertainties in the resulting map. Second, we fit and subtract new spatial templates that trace Galactic emission; in particular, we now use low-frequency WMAP data to trace synchrotron emission instead of the 408MHz sky survey. The WMAP point source catalog is updated to include 115 new sources whose detection is made possible by the improved sky map sensitivity. We derive the angular power spectrum of the temperature anisotropy using a hybrid approach that combines a maximum likelihood estimate at low l (large angular scales) with a quadratic cross-power estimate for l>30. The resulting multifrequency spectra are analyzed for residual point source contamination. At 94GHz the unmasked sources contribute 128+/-27^{micron}^K^2^ to l(l+1)C_l_/2{pi} at l=1000. After subtracting this contribution, our best estimate of the CMB power spectrum is derived by averaging cross-power spectra from 153 statistically independent channel pairs. A simple six-parameter {LAMBDA}CDM model continues to fit CMB data and other measures of large-scale structure remarkably well. The new polarization data produce a better measurement of the optical depth to reionization, {tau}=0.089+/-0.03. This new and tighter constraint on {tau} help break a degeneracy with the scalar spectral index, which is now found to be ns=0.960+/-0.016.